Modern Data Mining, HW 3

1 Case study 1: ISLR::Auto data

This will be the last part of the Auto data from ISLR. The original data contains 408 observations about cars. It has some similarity as the Cars data that we use in our lectures. To get the data, first install the package ISLR. The data set Auto should be loaded automatically. We use this case to go through methods learned so far.

Final modelling question: We want to explore the effects of each feature as best as possible.

1.1 Preparing variables:

1. You may explore the possibility of variable transformations. We normally do not suggest to transform \(x\) for the purpose of interpretation. You may consider to transform \(y\) to either correct the violation of the linear model assumptions or if you feel a transformation of \(y\) makes more sense from some theory. In this case we suggest you to look into GPM=1/MPG. Compare residual plots of MPG or GPM as responses and see which one might yield a more satisfactory patterns.

Auto <- ISLR::Auto
AutoCopy <- Auto
AutoCopy$mpg <- 1/Auto$mpg
colnames(AutoCopy)[which(colnames(AutoCopy) == "mpg")] <- "gpm"
model1 <- lm(mpg ~ horsepower + weight + year + as.factor(Auto$origin), data = Auto)
model2 <- lm(gpm ~ horsepower + weight + year + as.factor(AutoCopy$origin), data = AutoCopy)

res1 <- resid(model1) 
plot(fitted(model1), res1)
abline(0,0)

res2 <- resid(model2) 
plot(fitted(model2), res2) 
abline(0,0)

In addition, can you provide some background knowledge to support the notion: it makes more sense to model GPM?

From visual inspection of the two plots of the residuals, it is clear that there was uncaptured structure in the MPG fit while this uncaptured trend was somewhat picked up in the GPM plot. The residual plot in the former model is unbalanced: errors are all positive when y is small. The latter model with a reciprocal transformation solves this anomaly. The transformation makes sense because linear increases in weight would lead to increased fuel consumption, not fuel efficiency.

When using a linear or higher power model, it makes sense to have the response variable directly related, not inversely related.

2. You may also explore by adding interactions and higher order terms. The model(s) should be as parsimonious (simple) as possible, unless the gain in accuracy is significant from your point of view.

model3 <- lm(gpm ~ horsepower + weight + year + as.factor(AutoCopy$origin) + 
               (horsepower + weight + year)^2 + 
               I(horsepower^2) + I(horsepower^3) +
               I(weight^2) + I(weight^3) +
               I(year^2) + I(year^3)
               , data = AutoCopy)

model3.exh <- regsubsets(gpm ~ horsepower + weight + year + 
                           as.factor(AutoCopy$origin) + 
               (horsepower + weight + year)^2 + 
               I(horsepower^2) + I(horsepower^3) +
               I(weight^2) + I(weight^3) +
               I(year^2) + I(year^3)
               , data = AutoCopy,  nvmax=25, method="exhaustive")

f.e <- summary(model3.exh)
names(f.e)

## [1] "which"  "rsq"    "rss"    "adjr2"  "cp"     "bic"    "outmat" "obj"

str(f.e)

## List of 8
##  $ which : logi [1:14, 1:15] TRUE TRUE TRUE TRUE TRUE TRUE ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : chr [1:14] "1" "2" "3" "4" ...
##   .. ..$ : chr [1:15] "(Intercept)" "horsepower" "weight" "year" ...
##  $ rsq   : num [1:14] 0.785 0.878 0.883 0.885 0.887 ...
##  $ rss   : num [1:14] 0.0232 0.0132 0.0127 0.0125 0.0123 ...
##  $ adjr2 : num [1:14] 0.785 0.877 0.882 0.883 0.885 ...
##  $ cp    : num [1:14] 386.2 54.7 39.1 34.1 28.3 ...
##  $ bic   : num [1:14] -591 -806 -816 -817 -818 ...
##  $ outmat: chr [1:14, 1:14] " " " " " " " " ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : chr [1:14] "1  ( 1 )" "2  ( 1 )" "3  ( 1 )" "4  ( 1 )" ...
##   .. ..$ : chr [1:14] "horsepower" "weight" "year" "as.factor(AutoCopy$origin)2" ...
##  $ obj   :List of 28
##   ..$ np       : int 15
##   ..$ nrbar    : int 105
##   ..$ d        : num [1:15] 3.92e+02 1.23e+08 6.05e+01 2.94e+10 4.69e+11 ...
##   ..$ rbar     : num [1:105] 5.79e+03 2.02e-01 1.24e+04 2.25e+05 3.39e+05 ...
##   ..$ thetab   : num [1:15] 4.78e-02 -1.66e-05 -1.28e-02 1.13e-06 1.69e-07 ...
##   ..$ first    : int 2
##   ..$ last     : int 15
##   ..$ vorder   : int [1:15] 1 11 6 7 15 13 3 12 4 10 ...
##   ..$ tol      : num [1:15] 9.90e-09 6.53e-05 9.65e-09 2.44e-04 3.22e-03 ...
##   ..$ rss      : num [1:15] 0.1083 0.0743 0.0644 0.0267 0.0133 ...
##   ..$ bound    : num [1:15] 0.1083 0.0232 0.0132 0.0127 0.0125 ...
##   ..$ nvmax    : int 15
##   ..$ ress     : num [1:15, 1] 0.1083 0.0232 0.0132 0.0127 0.0125 ...
##   ..$ ir       : int 15
##   ..$ nbest    : int 1
##   ..$ lopt     : int [1:120, 1] 1 1 13 1 3 15 1 14 15 3 ...
##   ..$ il       : int 120
##   ..$ ier      : int 0
##   ..$ xnames   : chr [1:15] "(Intercept)" "horsepower" "weight" "year" ...
##   ..$ method   : chr "exhaustive"
##   ..$ force.in : Named logi [1:15] TRUE FALSE FALSE FALSE FALSE FALSE ...
##   .. ..- attr(*, "names")= chr [1:15] "" "horsepower" "weight" "year" ...
##   ..$ force.out: Named logi [1:15] FALSE FALSE FALSE FALSE FALSE FALSE ...
##   .. ..- attr(*, "names")= chr [1:15] "" "horsepower" "weight" "year" ...
##   ..$ sserr    : num 0.0113
##   ..$ intercept: logi TRUE
##   ..$ lindep   : logi [1:15] FALSE FALSE FALSE FALSE FALSE FALSE ...
##   ..$ nullrss  : num 0.108
##   ..$ nn       : int 392
##   ..$ call     : language regsubsets.formula(gpm ~ horsepower + weight + year + as.factor(AutoCopy$origin) +      (horsepower + weight + ye| __truncated__ ...
##   ..- attr(*, "class")= chr "regsubsets"
##  - attr(*, "class")= chr "summary.regsubsets"

plot(f.e$cp, xlab="Number of predictors", 
     ylab="Cp", col="red", pch=16)

model4 <- lm(gpm ~ horsepower + weight + year + as.factor(AutoCopy$origin) + 
               (horsepower + weight + year)^2 + 
               I(horsepower^2) + I(horsepower^3) +
               I(weight^2) + I(weight^3) 
               , data = AutoCopy)

model4.exh <- regsubsets(gpm ~ horsepower + weight + year + 
                           as.factor(AutoCopy$origin) + 
               (horsepower + weight + year)^2 + 
               I(horsepower^2) + I(horsepower^3) +
               I(weight^2) + I(weight^3)
               , data = AutoCopy,  nvmax=25, method="exhaustive")

f.e <- summary(model4.exh)
names(f.e)

## [1] "which"  "rsq"    "rss"    "adjr2"  "cp"     "bic"    "outmat" "obj"

str(f.e)

## List of 8
##  $ which : logi [1:12, 1:13] TRUE TRUE TRUE TRUE TRUE TRUE ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : chr [1:12] "1" "2" "3" "4" ...
##   .. ..$ : chr [1:13] "(Intercept)" "horsepower" "weight" "year" ...
##  $ rsq   : num [1:12] 0.785 0.878 0.883 0.885 0.886 ...
##  $ rss   : num [1:12] 0.0232 0.0132 0.0127 0.0125 0.0124 ...
##  $ adjr2 : num [1:12] 0.785 0.877 0.882 0.883 0.884 ...
##  $ cp    : num [1:12] 344.72 31.11 16.38 11.84 9.79 ...
##  $ bic   : num [1:12] -591 -806 -816 -817 -815 ...
##  $ outmat: chr [1:12, 1:12] " " " " " " " " ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : chr [1:12] "1  ( 1 )" "2  ( 1 )" "3  ( 1 )" "4  ( 1 )" ...
##   .. ..$ : chr [1:12] "horsepower" "weight" "year" "as.factor(AutoCopy$origin)2" ...
##  $ obj   :List of 28
##   ..$ np       : int 13
##   ..$ nrbar    : int 78
##   ..$ d        : num [1:13] 3.92e+02 3.09e+23 1.65e+07 1.84e+12 7.58e+07 ...
##   ..$ rbar     : num [1:78] 3.31e+10 2.98e+03 3.39e+05 7.88e+03 2.25e+05 ...
##   ..$ thetab   : num [1:13] 4.78e-02 5.16e-13 1.31e-05 3.95e-08 -5.66e-06 ...
##   ..$ first    : int 2
##   ..$ last     : int 13
##   ..$ vorder   : int [1:13] 1 10 3 11 12 13 4 7 8 6 ...
##   ..$ tol      : num [1:13] 9.90e-09 8.27e+02 4.10e-05 6.49e-03 1.10e-04 ...
##   ..$ rss      : num [1:13] 0.1083 0.0259 0.0231 0.0203 0.0178 ...
##   ..$ bound    : num [1:13] 0.1083 0.0232 0.0132 0.0127 0.0125 ...
##   ..$ nvmax    : int 13
##   ..$ ress     : num [1:13, 1] 0.1083 0.0232 0.0132 0.0127 0.0125 ...
##   ..$ ir       : int 13
##   ..$ nbest    : int 1
##   ..$ lopt     : int [1:91, 1] 1 1 11 1 13 3 1 13 3 12 ...
##   ..$ il       : int 91
##   ..$ ier      : int 0
##   ..$ xnames   : chr [1:13] "(Intercept)" "horsepower" "weight" "year" ...
##   ..$ method   : chr "exhaustive"
##   ..$ force.in : Named logi [1:13] TRUE FALSE FALSE FALSE FALSE FALSE ...
##   .. ..- attr(*, "names")= chr [1:13] "" "horsepower" "weight" "year" ...
##   ..$ force.out: Named logi [1:13] FALSE FALSE FALSE FALSE FALSE FALSE ...
##   .. ..- attr(*, "names")= chr [1:13] "" "horsepower" "weight" "year" ...
##   ..$ sserr    : num 0.012
##   ..$ intercept: logi TRUE
##   ..$ lindep   : logi [1:13] FALSE FALSE FALSE FALSE FALSE FALSE ...
##   ..$ nullrss  : num 0.108
##   ..$ nn       : int 392
##   ..$ call     : language regsubsets.formula(gpm ~ horsepower + weight + year + as.factor(AutoCopy$origin) +      (horsepower + weight + ye| __truncated__ ...
##   ..- attr(*, "class")= chr "regsubsets"
##  - attr(*, "class")= chr "summary.regsubsets"

plot(f.e$cp, xlab="Number of predictors", 
     ylab="Cp", col="red", pch=16)

3. Use Mallow’s \(C_p\) or BIC to select the model.

Using the “elbow” rule, the cp appears to level off around 6, so we will select 6 predictors as the chosen model.

After inspecting the variables chosen by the size 6 optimal model, the 3rd and fourth terms were found to be year squared and year cubed, one having a positive coefficient and the other having a negative coefficient. This is not easily interpreted (why does year squared decrease gpm but year cubed increase?)

For easier interpret ability, in the final mode, we elect to exclude higher order terms on year. After re-running the CP selection process, the new optimal model was found to be of size four (using the elbow rule).

1.2 Describe the final model and its accuracy. Include diagnostic plots with particular focus on the model residuals.

• Summarize the effects found.
• Predict the mpg of a car that is: built in 1983, in the US, red, 180 inches long, 8 cylinders, 350 displacement, 260 as horsepower, and weighs 4,000 pounds. Give a 95% CI.
• Any suggestions as to how to improve the quality of the study?

After eliminating year higher order terms due to interpretability issues, the optimal model found has terms

• weight increasing gpm
• horsepower:weight decreasing gpm
• horsepower:year increasing gpm
• weight:year decreasing gpm

This model is far more interpretable, with weight and horsepower*year having easy to interpret stories. As cars get heavier, they use more gas. As cars get newer and more powerful, they consume more gpm. As cars get heavier and newer, they consume less gpm compared to an older car of similar weight.

coef(model3.exh,6)

##     (Intercept)          weight            year       I(year^2)       I(year^3) 
##       -1.11e+01        4.35e-05        4.35e-01       -5.65e-03        2.44e-05 
## horsepower:year     weight:year 
##        1.16e-06       -4.20e-07

coef(model4.exh,4)

##       (Intercept)            weight horsepower:weight   horsepower:year 
##         -4.53e-03          5.60e-05         -2.43e-08          2.08e-06 
##       weight:year 
##         -5.43e-07

fit.final <- lm(gpm ~ weight  + horsepower:weight + horsepower:year + weight:year, AutoCopy )   
par(mfrow=c(1,2))
plot(fit.final, 1)
plot(fit.final, 2) 

newcar <- AutoCopy [1,] # Get the right format and the variable names
newcar$year <- 83
newcar$origin <- as.factor(1)
newcar$cylinders <- 8
newcar$displacement <-350
newcar$horsepower <- 260
newcar$weight <- 4000

newcar.gpm <- predict(fit.final, newcar, interval="confidence", se.fit=TRUE) 
newcar.gpm

## $fit
##      fit    lwr    upr
## 1 0.0585 0.0532 0.0638
## 
## $se.fit
## [1] 0.0027
## 
## $df
## [1] 387
## 
## $residual.scale
## [1] 0.00568

newcar.mpg <- 1/newcar.gpm$fit
newcar.mpg

##    fit  lwr  upr
## 1 17.1 18.8 15.7

The predicted MPG confidence interval ranges from 15.7 to 18.8mpg, with a fitted value of 17.1 mpg.

How we can improve the model?

Using principle components could possibly lead to a better “fit” at the expense of interpret ability. If we seek to retain a high level of interpret ability, we have to accept a bit of modeling error.

Perhaps most important, using clustering analysis to cluster similar automobiles could lead to a better result, since there are likely non-linear and non-polynomial influences of variables (no power of weight will pick up whether the car is a pickup truck or not, etc.)

2 Case study 2: COVID

# county-level socialeconomic information
county_data <- fread("data/covid_county.csv")
# county-level COVID case and death
covid_rate <- fread("data/covid_rates.csv")
# county-level lockdown dates
covid_intervention <- fread("data/covid_intervention.csv")

2.1 understand the data

view(dfSummary(covid_rate),method = "render")

Data Frame Summary

covid_rate

Dimensions: 1008984 x 8
Duplicates: 0

No	Variable	Stats / Values	Freqs (% of Valid)	Graph	Valid	Missing
1	FIPS [integer]	Mean (sd) : 30572 (15054) min ≤ med ≤ max: 1001 ≤ 29179 ≤ 56045 IQR (CV) : 26072 (0.5)	3108 distinct values		1008984 (100.0%)	0 (0.0%)
2	date [IDate, Date]	min : 2020-01-21 med : 2020-09-11 max : 2021-02-20 range : 1y 0m 30d	397 distinct values		1008984 (100.0%)	0 (0.0%)
3	County [character]	1. Washington 2. Jefferson 3. Franklin 4. Jackson 5. Lincoln 6. Madison 7. Montgomery 8. Union 9. Clay 10. Marion [ 1809 others ]	10358 ( 1.0% ) 8669 ( 0.9% ) 8282 ( 0.8% ) 7839 ( 0.8% ) 7801 ( 0.8% ) 6630 ( 0.7% ) 6035 ( 0.6% ) 5926 ( 0.6% ) 5862 ( 0.6% ) 5613 ( 0.6% ) 935969 ( 92.8% )		1008984 (100.0%)	0 (0.0%)
4	State [character]	1. Texas 2. Georgia 3. Virginia 4. Kentucky 5. Missouri 6. Illinois 7. North Carolina 8. Kansas 9. Iowa 10. Tennessee [ 39 others ]	79955 ( 7.9% ) 53032 ( 5.3% ) 43638 ( 4.3% ) 38890 ( 3.9% ) 36684 ( 3.6% ) 33241 ( 3.3% ) 33108 ( 3.3% ) 32113 ( 3.2% ) 32074 ( 3.2% ) 31543 ( 3.1% ) 594706 ( 58.9% )		1008984 (100.0%)	0 (0.0%)
5	cum_cases [integer]	Mean (sd) : 2933 (14747) min ≤ med ≤ max: 0 ≤ 366 ≤ 1179633 IQR (CV) : 1503 (5)	39874 distinct values		1008984 (100.0%)	0 (0.0%)
6	cum_deaths [integer]	Mean (sd) : 65.6 (323) min ≤ med ≤ max: 0 ≤ 7 ≤ 19793 IQR (CV) : 30 (4.9)	4494 distinct values		1008984 (100.0%)	0 (0.0%)
7	week [integer]	Mean (sd) : 34.1 (13.6) min ≤ med ≤ max: 1 ≤ 34 ≤ 57 IQR (CV) : 23 (0.4)	57 distinct values		1008984 (100.0%)	0 (0.0%)
8	TotalPopEst2019 [integer]	Mean (sd) : 112405 (356633) min ≤ med ≤ max: 169 ≤ 27772 ≤ 1e+07 IQR (CV) : 62056 (3.2)	3057 distinct values		1008984 (100.0%)	0 (0.0%)

Generated by summarytools 1.0.0 (R version 4.1.2)
2022-02-27

view(dfSummary(county_data),method = "render")

Data Frame Summary

county_data

Dimensions: 3279 x 208
Duplicates: 0

No	Variable	Stats / Values	Freqs (% of Valid)	Graph	Valid	Missing
1	FIPS [integer]	Mean (sd) : 31342 (16341) min ≤ med ≤ max: 0 ≤ 30019 ≤ 72153 IQR (CV) : 27082 (0.5)	3278 distinct values		3279 (100.0%)	0 (0.0%)
2	State [character]	1. TX 2. GA 3. VA 4. KY 5. MO 6. KS 7. IL 8. NC 9. IA 10. TN [ 43 others ]	255 ( 7.8% ) 160 ( 4.9% ) 135 ( 4.1% ) 121 ( 3.7% ) 116 ( 3.5% ) 106 ( 3.2% ) 103 ( 3.1% ) 101 ( 3.1% ) 100 ( 3.0% ) 96 ( 2.9% ) 1986 ( 60.6% )		3279 (100.0%)	0 (0.0%)
3	County [character]	1. Washington 2. Franklin 3. Jefferson 4. Jackson 5. Lincoln 6. Madison 7. Clay 8. Montgomery 9. Union 10. Marion [ 1937 others ]	32 ( 1.0% ) 26 ( 0.8% ) 26 ( 0.8% ) 24 ( 0.7% ) 24 ( 0.7% ) 20 ( 0.6% ) 18 ( 0.5% ) 18 ( 0.5% ) 18 ( 0.5% ) 17 ( 0.5% ) 3056 ( 93.2% )		3279 (100.0%)	0 (0.0%)
4	MedHHInc [integer]	Mean (sd) : 52945 (13879) min ≤ med ≤ max: 25385 ≤ 50748 ≤ 140382 IQR (CV) : 15237 (0.3)	3081 distinct values		3193 (97.4%)	86 (2.6%)
5	PerCapitaInc [integer]	Mean (sd) : 26720 (6948) min ≤ med ≤ max: 5974 ≤ 26169 ≤ 72832 IQR (CV) : 7553 (0.3)	3021 distinct values		3273 (99.8%)	6 (0.2%)
6	PovertyUnder18Pct [numeric]	Mean (sd) : 21 (8.9) min ≤ med ≤ max: 2.5 ≤ 20.1 ≤ 68.3 IQR (CV) : 11.7 (0.4)	425 distinct values		3193 (97.4%)	86 (2.6%)
7	PovertyAllAgesPct [numeric]	Mean (sd) : 15.1 (6.1) min ≤ med ≤ max: 2.6 ≤ 14.1 ≤ 54 IQR (CV) : 7.5 (0.4)	317 distinct values		3193 (97.4%)	86 (2.6%)
8	Deep_Pov_All [numeric]	Mean (sd) : 7.1 (4.6) min ≤ med ≤ max: 0 ≤ 6.2 ≤ 44 IQR (CV) : 3.7 (0.6)	3270 distinct values		3273 (99.8%)	6 (0.2%)
9	Deep_Pov_Children [numeric]	Mean (sd) : 10.2 (7.5) min ≤ med ≤ max: 0 ≤ 8.7 ≤ 69.2 IQR (CV) : 7.1 (0.7)	3222 distinct values		3272 (99.8%)	7 (0.2%)
10	PovertyUnder18Num [integer]	Mean (sd) : 12212 (235886) min ≤ med ≤ max: 5 ≤ 1200 ≤ 1.3e+07 IQR (CV) : 2463 (19.3)	2264 distinct values		3193 (97.4%)	86 (2.6%)
11	PovertyAllAgesNum [integer]	Mean (sd) : 39323 (758374) min ≤ med ≤ max: 5 ≤ 3876 ≤ 41852315 IQR (CV) : 8253 (19.3)	2803 distinct values		3193 (97.4%)	86 (2.6%)
12	PopChangeRate1819 [numeric]	Mean (sd) : 0.1 (1.3) min ≤ med ≤ max: -15.5 ≤ 0 ≤ 14.2 IQR (CV) : 1.2 (13.3)	2182 distinct values		3195 (97.4%)	84 (2.6%)
13	PopChangeRate1019 [numeric]	Mean (sd) : 0.7 (8.9) min ≤ med ≤ max: -33.5 ≤ -0.6 ≤ 134 IQR (CV) : 8.9 (12.7)	3058 distinct values		3273 (99.8%)	6 (0.2%)
14	TotalPopEst2019 [integer]	Mean (sd) : 301847 (5867536) min ≤ med ≤ max: 86 ≤ 26687 ≤ 3.28e+08 IQR (CV) : 60369 (19.4)	3216 distinct values		3273 (99.8%)	6 (0.2%)
15	NetMigrationRate1019 [numeric]	Mean (sd) : 0 (7.6) min ≤ med ≤ max: -32.2 ≤ -1.1 ≤ 116 IQR (CV) : 7.2 (1427)	2937 distinct values		3194 (97.4%)	85 (2.6%)
16	NaturalChangeRate1019 [numeric]	Mean (sd) : 1 (3.7) min ≤ med ≤ max: -11 ≤ 0.6 ≤ 23.1 IQR (CV) : 4.4 (3.5)	2815 distinct values		3194 (97.4%)	85 (2.6%)
17	Net_International_Migration_Rate_2010_2019 [numeric]	Mean (sd) : 0.9 (1.6) min ≤ med ≤ max: -1.2 ≤ 0.4 ≤ 21.3 IQR (CV) : 1 (1.8)	1801 distinct values		3194 (97.4%)	85 (2.6%)
18	PopChangeRate0010 [numeric]	Mean (sd) : 5.2 (13) min ≤ med ≤ max: -46.6 ≤ 3.2 ≤ 110 IQR (CV) : 12.7 (2.5)	2197 distinct values		3267 (99.6%)	12 (0.4%)
19	NetMigrationRate0010 [numeric]	Mean (sd) : 1 (11.1) min ≤ med ≤ max: -57.4 ≤ -0.3 ≤ 85.2 IQR (CV) : 10.5 (11.2)	2053 distinct values		3184 (97.1%)	95 (2.9%)
20	NaturalChangeRate0010 [numeric]	Mean (sd) : 2.8 (4.7) min ≤ med ≤ max: -14.5 ≤ 2.4 ≤ 26.4 IQR (CV) : 5.5 (1.7)	1457 distinct values		3184 (97.1%)	95 (2.9%)
21	Immigration_Rate_2000_2010 [numeric]	Mean (sd) : 1.3 (1.8) min ≤ med ≤ max: -5.2 ≤ 0.6 ≤ 17.7 IQR (CV) : 1.4 (1.5)	3161 distinct values		3184 (97.1%)	95 (2.9%)
22	PopDensity2010 [numeric]	Mean (sd) : 285 (1717) min ≤ med ≤ max: 0 ≤ 47 ≤ 69468 IQR (CV) : 114 (6)	2967 distinct values		3273 (99.8%)	6 (0.2%)
23	Under18Pct2010 [numeric]	Mean (sd) : 23.5 (3.3) min ≤ med ≤ max: 0 ≤ 23.4 ≤ 41.6 IQR (CV) : 3.6 (0.1)	1169 distinct values		3273 (99.8%)	6 (0.2%)
24	Age65AndOlderPct2010 [numeric]	Mean (sd) : 15.8 (4.1) min ≤ med ≤ max: 3.5 ≤ 15.4 ≤ 43.4 IQR (CV) : 5 (0.3)	1381 distinct values		3273 (99.8%)	6 (0.2%)
25	WhiteNonHispanicPct2010 [numeric]	Mean (sd) : 76.3 (22.9) min ≤ med ≤ max: 0.2 ≤ 85 ≤ 99.2 IQR (CV) : 28.7 (0.3)	2305 distinct values		3273 (99.8%)	6 (0.2%)
26	BlackNonHispanicPct2010 [numeric]	Mean (sd) : 8.6 (14.3) min ≤ med ≤ max: 0 ≤ 1.8 ≤ 85.4 IQR (CV) : 9.1 (1.7)	1404 distinct values		3273 (99.8%)	6 (0.2%)
27	AsianNonHispanicPct2010 [numeric]	Mean (sd) : 1.2 (2.5) min ≤ med ≤ max: 0 ≤ 0.5 ≤ 43 IQR (CV) : 0.7 (2.2)	499 distinct values		3273 (99.8%)	6 (0.2%)
28	NativeAmericanNonHispanicPct2010 [numeric]	Mean (sd) : 1.8 (7.5) min ≤ med ≤ max: 0 ≤ 0.3 ≤ 95 IQR (CV) : 0.4 (4.1)	485 distinct values		3273 (99.8%)	6 (0.2%)
29	HispanicPct2010 [numeric]	Mean (sd) : 10.5 (19) min ≤ med ≤ max: 0 ≤ 3.5 ≤ 99.7 IQR (CV) : 7.5 (1.8)	1440 distinct values		3273 (99.8%)	6 (0.2%)
30	MultipleRacePct2010 [numeric]	Mean (sd) : 2 (1.6) min ≤ med ≤ max: 0.1 ≤ 1.6 ≤ 29.5 IQR (CV) : 1.2 (0.8)	538 distinct values		3273 (99.8%)	6 (0.2%)
31	NonHispanicWhitePopChangeRate0010 [numeric]	Mean (sd) : 0.5 (13.8) min ≤ med ≤ max: -94.3 ≤ -0.7 ≤ 149 IQR (CV) : 12.3 (25.7)	2200 distinct values		3267 (99.6%)	12 (0.4%)
32	NonHispanicBlackPopChangeRate0010 [numeric]	Mean (sd) : 69.6 (485) min ≤ med ≤ max: -100 ≤ 13.6 ≤ 21950 IQR (CV) : 64.6 (7)	2444 distinct values		3206 (97.8%)	73 (2.2%)
33	NonHispanicAsianPopChangeRate0010 [numeric]	Mean (sd) : 74.2 (129) min ≤ med ≤ max: -100 ≤ 47.3 ≤ 2900 IQR (CV) : 73.8 (1.7)	2257 distinct values		3228 (98.4%)	51 (1.6%)
34	NonHispanicNativeAmericanPopChangeRate0010 [numeric]	Mean (sd) : 17.7 (66.4) min ≤ med ≤ max: -100 ≤ 9.1 ≤ 1500 IQR (CV) : 39 (3.8)	2182 distinct values		3244 (98.9%)	35 (1.1%)
35	HispanicPopChangeRate0010 [numeric]	Mean (sd) : 81.9 (91) min ≤ med ≤ max: -100 ≤ 66.4 ≤ 1740 IQR (CV) : 73.9 (1.1)	2947 distinct values		3267 (99.6%)	12 (0.4%)
36	MultipleRacePopChangeRate0010 [numeric]	Mean (sd) : 59.2 (57.2) min ≤ med ≤ max: -87.5 ≤ 53.5 ≤ 850 IQR (CV) : 58.8 (1)	2793 distinct values		3265 (99.6%)	14 (0.4%)
37	WhiteNonHispanicNum2010 [integer]	Mean (sd) : 180408 (3498477) min ≤ med ≤ max: 24 ≤ 19996 ≤ 1.97e+08 IQR (CV) : 47308 (19.4)	3201 distinct values		3273 (99.8%)	6 (0.2%)
38	BlackNonHispanicNum2010 [integer]	Mean (sd) : 34544 (675236) min ≤ med ≤ max: 0 ≤ 664 ≤ 37685848 IQR (CV) : 5466 (19.5)	1999 distinct values		3273 (99.8%)	6 (0.2%)
39	AsianNonHispanicNum2010 [integer]	Mean (sd) : 13260 (271334) min ≤ med ≤ max: 0 ≤ 115 ≤ 14465124 IQR (CV) : 635 (20.5)	1251 distinct values		3273 (99.8%)	6 (0.2%)
40	NativeAmericanNonHispanicNum2010 [integer]	Mean (sd) : 2060 (40450) min ≤ med ≤ max: 0 ≤ 100 ≤ 2247098 IQR (CV) : 367 (19.6)	1057 distinct values		3273 (99.8%)	6 (0.2%)
41	HispanicNum2010 [integer]	Mean (sd) : 47407 (944224) min ≤ med ≤ max: 0 ≤ 1001 ≤ 50477594 IQR (CV) : 4884 (19.9)	2259 distinct values		3273 (99.8%)	6 (0.2%)
42	MultipleRaceNum2010 [integer]	Mean (sd) : 8295 (162882) min ≤ med ≤ max: 1 ≤ 432 ≤ 9009073 IQR (CV) : 1357 (19.6)	1724 distinct values		3273 (99.8%)	6 (0.2%)
43	ForeignBornPct [numeric]	Mean (sd) : 4.8 (5.7) min ≤ med ≤ max: 0 ≤ 2.8 ≤ 53.3 IQR (CV) : 4.5 (1.2)	3180 distinct values		3194 (97.4%)	85 (2.6%)
44	ForeignBornEuropePct [numeric]	Mean (sd) : 0.6 (0.7) min ≤ med ≤ max: 0 ≤ 0.3 ≤ 7.7 IQR (CV) : 0.5 (1.3)	2991 distinct values		3194 (97.4%)	85 (2.6%)
45	ForeignBornMexPct [numeric]	Mean (sd) : 1.9 (3.5) min ≤ med ≤ max: 0 ≤ 0.6 ≤ 39.5 IQR (CV) : 1.8 (1.8)	2920 distinct values		3194 (97.4%)	85 (2.6%)
46	NonEnglishHHPct [numeric]	Mean (sd) : 3.6 (11.3) min ≤ med ≤ max: 0 ≤ 0.9 ≤ 89.5 IQR (CV) : 2 (3.2)	2986 distinct values		3273 (99.8%)	6 (0.2%)
47	Ed1LessThanHSPct [numeric]	Mean (sd) : 13.7 (6.6) min ≤ med ≤ max: 1.2 ≤ 12.2 ≤ 66.3 IQR (CV) : 8.8 (0.5)	3270 distinct values		3273 (99.8%)	6 (0.2%)
48	Ed2HSDiplomaOnlyPct [numeric]	Mean (sd) : 34.1 (7.2) min ≤ med ≤ max: 5.5 ≤ 34.3 ≤ 55.6 IQR (CV) : 9.5 (0.2)	3265 distinct values		3273 (99.8%)	6 (0.2%)
49	Ed3SomeCollegePct [numeric]	Mean (sd) : 21.6 (4.1) min ≤ med ≤ max: 4.1 ≤ 21.6 ≤ 38.7 IQR (CV) : 5 (0.2)	3270 distinct values		3273 (99.8%)	6 (0.2%)
50	Ed4AssocDegreePct [numeric]	Mean (sd) : 8.9 (2.6) min ≤ med ≤ max: 1.1 ≤ 8.7 ≤ 21.4 IQR (CV) : 3.4 (0.3)	3266 distinct values		3273 (99.8%)	6 (0.2%)
51	Ed5CollegePlusPct [numeric]	Mean (sd) : 21.7 (9.4) min ≤ med ≤ max: 0 ≤ 19.5 ≤ 78.5 IQR (CV) : 10.8 (0.4)	3271 distinct values		3273 (99.8%)	6 (0.2%)
52	AvgHHSize [numeric]	Mean (sd) : 2.5 (0.3) min ≤ med ≤ max: 1.3 ≤ 2.5 ≤ 5 IQR (CV) : 0.3 (0.1)	183 distinct values		3273 (99.8%)	6 (0.2%)
53	FemaleHHPct [numeric]	Mean (sd) : 11.4 (4.6) min ≤ med ≤ max: 0 ≤ 10.6 ≤ 40.8 IQR (CV) : 5 (0.4)	3260 distinct values		3273 (99.8%)	6 (0.2%)
54	HH65PlusAlonePct [numeric]	Mean (sd) : 12.6 (3.1) min ≤ med ≤ max: 2.8 ≤ 12.4 ≤ 31.8 IQR (CV) : 3.7 (0.2)	3258 distinct values		3273 (99.8%)	6 (0.2%)
55	OwnHomePct [numeric]	Mean (sd) : 71.3 (8.2) min ≤ med ≤ max: 4.3 ≤ 72.4 ≤ 92.4 IQR (CV) : 9.5 (0.1)	3269 distinct values		3273 (99.8%)	6 (0.2%)
56	ForeignBornNum [integer]	Mean (sd) : 40884 (812006) min ≤ med ≤ max: 0 ≤ 672 ≤ 43538827 IQR (CV) : 3000 (19.9)	2026 distinct values		3195 (97.4%)	84 (2.6%)
57	TotalPopACS [integer]	Mean (sd) : 297005 (5772068) min ≤ med ≤ max: 75 ≤ 26719 ≤ 3.23e+08 IQR (CV) : 59948 (19.4)	3210 distinct values		3273 (99.8%)	6 (0.2%)
58	ForeignBornAfricaPct [numeric]	Mean (sd) : 2.8 (145) min ≤ med ≤ max: 0 ≤ 0.1 ≤ 8182 IQR (CV) : 0.2 (52.3)	2101 distinct values		3195 (97.4%)	84 (2.6%)
59	Ed3SomeCollegeNum [integer]	Mean (sd) : 41363 (804615) min ≤ med ≤ max: 12 ≤ 3753 ≤ 4.5e+07 IQR (CV) : 8834 (19.5)	2889 distinct values		3273 (99.8%)	6 (0.2%)
60	Ed2HSDiplomaOnlyNum [integer]	Mean (sd) : 54532 (1056336) min ≤ med ≤ max: 15 ≤ 6578 ≤ 59265308 IQR (CV) : 12964 (19.4)	3020 distinct values		3273 (99.8%)	6 (0.2%)
61	Ed1LessThanHSNum [integer]	Mean (sd) : 24885 (486088) min ≤ med ≤ max: 4 ≤ 2652 ≤ 26948057 IQR (CV) : 5234 (19.5)	2712 distinct values		3272 (99.8%)	7 (0.2%)
62	TotalPop25Plus [integer]	Mean (sd) : 200959 (3904200) min ≤ med ≤ max: 69 ≤ 18362 ≤ 2.18e+08 IQR (CV) : 39924 (19.4)	3180 distinct values		3273 (99.8%)	6 (0.2%)
63	Ed5CollegePlusNum [integer]	Mean (sd) : 63309 (1232394) min ≤ med ≤ max: 0 ≤ 3323 ≤ 68867051 IQR (CV) : 9897 (19.5)	2829 distinct values		3273 (99.8%)	6 (0.2%)
64	TotalOccHU [integer]	Mean (sd) : 110145 (2137025) min ≤ med ≤ max: 33 ≤ 10202 ≤ 1.2e+08 IQR (CV) : 22737 (19.4)	3103 distinct values		3272 (99.8%)	7 (0.2%)
65	ForeignBornAsiaPct [numeric]	Mean (sd) : 1.7 (31.7) min ≤ med ≤ max: 0 ≤ 0.5 ≤ 1791 IQR (CV) : 0.9 (19.2)	2954 distinct values		3195 (97.4%)	84 (2.6%)
66	Ed4AssocDegreeNum [integer]	Mean (sd) : 16886 (327446) min ≤ med ≤ max: 7 ≤ 1593 ≤ 18338323 IQR (CV) : 3943 (19.4)	2501 distinct values		3272 (99.8%)	7 (0.2%)
67	ForeignBornEuropeNum [integer]	Mean (sd) : 4487 (87789) min ≤ med ≤ max: 0 ≤ 83 ≤ 4778170 IQR (CV) : 367 (19.6)	1072 distinct values		3195 (97.4%)	84 (2.6%)
68	NonEnglishHHNum [integer]	Mean (sd) : 5134 (98171) min ≤ med ≤ max: 0 ≤ 89 ≤ 5323080 IQR (CV) : 457 (19.1)	1155 distinct values		3273 (99.8%)	6 (0.2%)
69	HH65PlusAloneNum [integer]	Mean (sd) : 11843 (229373) min ≤ med ≤ max: 4 ≤ 1266 ≤ 12868890 IQR (CV) : 2557 (19.4)	2351 distinct values		3273 (99.8%)	6 (0.2%)
70	OwnHomeNum [integer]	Mean (sd) : 70322 (1361695) min ≤ med ≤ max: 2 ≤ 7314 ≤ 76444810 IQR (CV) : 15723 (19.4)	3061 distinct values		3273 (99.8%)	6 (0.2%)
71	FemaleHHNum [integer]	Mean (sd) : 13891 (269278) min ≤ med ≤ max: 0 ≤ 1189 ≤ 15058180 IQR (CV) : 2778 (19.4)	2316 distinct values		3273 (99.8%)	6 (0.2%)
72	TotalHH [integer]	Mean (sd) : 110145 (2137025) min ≤ med ≤ max: 33 ≤ 10202 ≤ 1.2e+08 IQR (CV) : 22737 (19.4)	3103 distinct values		3272 (99.8%)	7 (0.2%)
73	ForeignBornCentralSouthAmPct [numeric]	Mean (sd) : 2.5 (3.9) min ≤ med ≤ max: 0 ≤ 1.1 ≤ 39.5 IQR (CV) : 2.4 (1.6)	3035 distinct values		3194 (97.4%)	85 (2.6%)
74	ForeignBornCentralSouthAmNum [integer]	Mean (sd) : 16796 (339763) min ≤ med ≤ max: 0 ≤ 280 ≤ 17881956 IQR (CV) : 1440 (20.2)	1565 distinct values		3194 (97.4%)	85 (2.6%)
75	ForeignBornCaribPct [numeric]	Mean (sd) : 0.2 (1) min ≤ med ≤ max: 0 ≤ 0 ≤ 32 IQR (CV) : 0.2 (4.2)	1951 distinct values		3194 (97.4%)	85 (2.6%)
76	ForeignBornCaribNum [integer]	Mean (sd) : 3993 (85882) min ≤ med ≤ max: 0 ≤ 10 ≤ 4251037 IQR (CV) : 88 (21.5)	665 distinct values		3194 (97.4%)	85 (2.6%)
77	ForeignBornAfricaNum [integer]	Mean (sd) : 2021 (39190) min ≤ med ≤ max: 0 ≤ 13 ≤ 2151409 IQR (CV) : 109 (19.4)	735 distinct values		3194 (97.4%)	85 (2.6%)
78	ForeignBornAsiaNum [integer]	Mean (sd) : 12585 (252757) min ≤ med ≤ max: 0 ≤ 122 ≤ 13398520 IQR (CV) : 648 (20.1)	1256 distinct values		3194 (97.4%)	85 (2.6%)
79	ForeignBornMexNum [integer]	Mean (sd) : 10702 (222034) min ≤ med ≤ max: 0 ≤ 186 ≤ 11394459 IQR (CV) : 928 (20.7)	1399 distinct values		3194 (97.4%)	85 (2.6%)
80	LandAreaSQMiles2010 [numeric]	Mean (sd) : 3240 (63263) min ≤ med ≤ max: 2 ≤ 610 ≤ 3531905 IQR (CV) : 511 (19.5)	3235 distinct values		3273 (99.8%)	6 (0.2%)
81	Age65AndOlderNum2010 [integer]	Mean (sd) : 37087 (718626) min ≤ med ≤ max: 12 ≤ 4112 ≤ 40267984 IQR (CV) : 8177 (19.4)	2908 distinct values		3273 (99.8%)	6 (0.2%)
82	TotalPop2010 [numeric]	Mean (sd) : 284130 (5517126) min ≤ med ≤ max: 68.2 ≤ 26890 ≤ 3.09e+08 IQR (CV) : 58668 (19.4)	3220 distinct values		3273 (99.8%)	6 (0.2%)
83	Under18Num2010 [integer]	Mean (sd) : 68273 (1326626) min ≤ med ≤ max: 0 ≤ 6359 ≤ 74181467 IQR (CV) : 13681 (19.4)	3046 distinct values		3273 (99.8%)	6 (0.2%)
84	Net_International_Migration_2000_2010 [numeric]	Mean (sd) : 5973 (51531) min ≤ med ≤ max: -4973 ≤ 137 ≤ 1906302 IQR (CV) : 704 (8.6)	1625 distinct values		3184 (97.1%)	95 (2.9%)
85	NaturalChangeNum0010 [numeric]	Mean (sd) : 10719 (82811) min ≤ med ≤ max: -27273 ≤ 491 ≤ 3097661 IQR (CV) : 2574 (7.7)	2616 distinct values		3184 (97.1%)	95 (2.9%)
86	NetMigrationNum0010 [numeric]	Mean (sd) : 5975 (70245) min ≤ med ≤ max: -838668 ≤ -62.5 ≤ 2114643 IQR (CV) : 2704 (11.8)	2835 distinct values		3184 (97.1%)	95 (2.9%)
87	TotalPopEst2012 [integer]	Mean (sd) : 288777 (5608652) min ≤ med ≤ max: 86 ≤ 26901 ≤ 3.14e+08 IQR (CV) : 59167 (19.4)	3212 distinct values		3273 (99.8%)	6 (0.2%)
88	TotalPopEst2013 [integer]	Mean (sd) : 290747 (5647610) min ≤ med ≤ max: 89 ≤ 26886 ≤ 3.16e+08 IQR (CV) : 59451 (19.4)	3208 distinct values		3273 (99.8%)	6 (0.2%)
89	TotalPopEst2010 [integer]	Mean (sd) : 284671 (5527443) min ≤ med ≤ max: 84 ≤ 26854 ≤ 3.09e+08 IQR (CV) : 58777 (19.4)	3220 distinct values		3273 (99.8%)	6 (0.2%)
90	TotalPopEst2014 [integer]	Mean (sd) : 292843 (5689251) min ≤ med ≤ max: 89 ≤ 26944 ≤ 3.18e+08 IQR (CV) : 59489 (19.4)	3208 distinct values		3273 (99.8%)	6 (0.2%)
91	TotalPopEst2011 [integer]	Mean (sd) : 286706 (5567688) min ≤ med ≤ max: 90 ≤ 26826 ≤ 3.12e+08 IQR (CV) : 59129 (19.4)	3211 distinct values		3273 (99.8%)	6 (0.2%)
92	Net_International_Migration_2010_2019 [integer]	Mean (sd) : 7219 (141089) min ≤ med ≤ max: -1451 ≤ 81 ≤ 7685444 IQR (CV) : 503 (19.5)	1261 distinct values		3194 (97.4%)	85 (2.6%)
93	NaturalChange1019 [integer]	Mean (sd) : 10550 (206980) min ≤ med ≤ max: -30357 ≤ 83.5 ≤ 11232413 IQR (CV) : 1510 (19.6)	2134 distinct values		3194 (97.4%)	85 (2.6%)
94	TotalPopEst2015 [integer]	Mean (sd) : 294964 (5731377) min ≤ med ≤ max: 88 ≤ 26827 ≤ 3.21e+08 IQR (CV) : 59646 (19.4)	3204 distinct values		3273 (99.8%)	6 (0.2%)
95	TotalPopEst2016 [integer]	Mean (sd) : 297057 (5772826) min ≤ med ≤ max: 88 ≤ 26626 ≤ 3.23e+08 IQR (CV) : 59973 (19.4)	3213 distinct values		3273 (99.8%)	6 (0.2%)
96	TotalPopEst2017 [integer]	Mean (sd) : 298905 (5809474) min ≤ med ≤ max: 86 ≤ 26676 ≤ 3.25e+08 IQR (CV) : 60010 (19.4)	3207 distinct values		3273 (99.8%)	6 (0.2%)
97	NetMigration1019 [integer]	Mean (sd) : 7219 (150698) min ≤ med ≤ max: -678325 ≤ -146 ≤ 7685444 IQR (CV) : 1830 (20.9)	2476 distinct values		3194 (97.4%)	85 (2.6%)
98	TotalPopEst2018 [integer]	Mean (sd) : 3e+05 (5839861) min ≤ med ≤ max: 86 ≤ 26702 ≤ 3.27e+08 IQR (CV) : 59824 (19.4)	3219 distinct values		3273 (99.8%)	6 (0.2%)
99	TotalPopEstBase2010 [integer]	Mean (sd) : 284230 (5518191) min ≤ med ≤ max: 82 ≤ 26908 ≤ 3.09e+08 IQR (CV) : 58771 (19.4)	3207 distinct values		3272 (99.8%)	7 (0.2%)
100	UnempRate2019 [numeric]	Mean (sd) : 4.1 (1.8) min ≤ med ≤ max: 0.7 ≤ 3.7 ≤ 19.3 IQR (CV) : 1.7 (0.4)	123 distinct values		3272 (99.8%)	7 (0.2%)
101	UnempRate2018 [numeric]	Mean (sd) : 4.3 (1.9) min ≤ med ≤ max: 1.3 ≤ 3.9 ≤ 19.6 IQR (CV) : 1.8 (0.4)	131 distinct values		3272 (99.8%)	7 (0.2%)
102	UnempRate2017 [numeric]	Mean (sd) : 4.8 (2.2) min ≤ med ≤ max: 1.6 ≤ 4.4 ≤ 20.6 IQR (CV) : 1.9 (0.5)	145 distinct values		3272 (99.8%)	7 (0.2%)
103	UnempRate2016 [numeric]	Mean (sd) : 5.4 (2.4) min ≤ med ≤ max: 1.7 ≤ 5 ≤ 24.1 IQR (CV) : 2.2 (0.4)	150 distinct values		3272 (99.8%)	7 (0.2%)
104	UnempRate2015 [numeric]	Mean (sd) : 5.7 (2.5) min ≤ med ≤ max: 1.8 ≤ 5.3 ≤ 24.5 IQR (CV) : 2.4 (0.4)	152 distinct values		3272 (99.8%)	7 (0.2%)
105	UnempRate2014 [numeric]	Mean (sd) : 6.5 (2.9) min ≤ med ≤ max: 1.2 ≤ 6.1 ≤ 26.4 IQR (CV) : 2.9 (0.4)	178 distinct values		3272 (99.8%)	7 (0.2%)
106	UnempRate2010 [numeric]	Mean (sd) : 9.6 (3.5) min ≤ med ≤ max: 2.1 ≤ 9.3 ≤ 28.8 IQR (CV) : 4.2 (0.4)	203 distinct values		3272 (99.8%)	7 (0.2%)
107	UnempRate2007 [numeric]	Mean (sd) : 5.1 (2.1) min ≤ med ≤ max: 1.5 ≤ 4.7 ≤ 20.4 IQR (CV) : 2.1 (0.4)	138 distinct values		3267 (99.6%)	12 (0.4%)
108	PctEmpChange1019 [numeric]	Mean (sd) : 4.9 (17.5) min ≤ med ≤ max: -34.1 ≤ 3.9 ≤ 703 IQR (CV) : 13.7 (3.6)	2221 distinct values		3272 (99.8%)	7 (0.2%)
109	PctEmpChange1819 [numeric]	Mean (sd) : 0.8 (3) min ≤ med ≤ max: -28.8 ≤ 0.8 ≤ 104 IQR (CV) : 2.1 (3.8)	834 distinct values		3272 (99.8%)	7 (0.2%)
110	PctEmpChange0719 [numeric]	Mean (sd) : -0.3 (28.7) min ≤ med ≤ max: -59.2 ≤ -1.7 ≤ 1316 IQR (CV) : 17.6 (-104)	2395 distinct values		3267 (99.6%)	12 (0.4%)
111	PctEmpChange0710 [numeric]	Mean (sd) : -5.2 (10.3) min ≤ med ≤ max: -55 ≤ -5.3 ≤ 91.6 IQR (CV) : 10.1 (-2)	2053 distinct values		3267 (99.6%)	12 (0.4%)
112	PctEmpAgriculture [numeric]	Mean (sd) : 5 (6.2) min ≤ med ≤ max: 0 ≤ 2.8 ≤ 59.6 IQR (CV) : 5 (1.3)	3256 distinct values		3272 (99.8%)	7 (0.2%)
113	PctEmpMining [numeric]	Mean (sd) : 1.5 (3.4) min ≤ med ≤ max: 0 ≤ 0.3 ≤ 44 IQR (CV) : 1.2 (2.2)	2885 distinct values		3272 (99.8%)	7 (0.2%)
114	PctEmpConstruction [numeric]	Mean (sd) : 7.3 (2.4) min ≤ med ≤ max: 0 ≤ 7 ≤ 25.5 IQR (CV) : 2.7 (0.3)	3261 distinct values		3272 (99.8%)	7 (0.2%)
115	PctEmpManufacturing [numeric]	Mean (sd) : 12.2 (7.1) min ≤ med ≤ max: 0 ≤ 11.3 ≤ 51.7 IQR (CV) : 9.7 (0.6)	3260 distinct values		3272 (99.8%)	7 (0.2%)
116	PctEmpTrade [numeric]	Mean (sd) : 13.7 (2.7) min ≤ med ≤ max: 0.8 ≤ 13.9 ≤ 38.9 IQR (CV) : 3 (0.2)	3265 distinct values		3272 (99.8%)	7 (0.2%)
117	PctEmpTrans [numeric]	Mean (sd) : 5.5 (2.1) min ≤ med ≤ max: 0 ≤ 5.2 ≤ 27.7 IQR (CV) : 2.4 (0.4)	3259 distinct values		3272 (99.8%)	7 (0.2%)
118	PctEmpInformation [numeric]	Mean (sd) : 1.4 (0.8) min ≤ med ≤ max: 0 ≤ 1.3 ≤ 12.3 IQR (CV) : 0.9 (0.6)	3175 distinct values		3272 (99.8%)	7 (0.2%)
119	PctEmpFIRE [numeric]	Mean (sd) : 4.6 (1.9) min ≤ med ≤ max: 0 ≤ 4.3 ≤ 20.6 IQR (CV) : 2.2 (0.4)	3249 distinct values		3272 (99.8%)	7 (0.2%)
120	PctEmpServices [numeric]	Mean (sd) : 43.1 (7) min ≤ med ≤ max: 8.3 ≤ 43 ≤ 81.6 IQR (CV) : 9.3 (0.2)	3269 distinct values		3272 (99.8%)	7 (0.2%)
121	PctEmpGovt [numeric]	Mean (sd) : 5.7 (3.3) min ≤ med ≤ max: 0 ≤ 4.8 ≤ 38.6 IQR (CV) : 3.2 (0.6)	3266 distinct values		3272 (99.8%)	7 (0.2%)
122	NumCivEmployed [integer]	Mean (sd) : 140356 (2730225) min ≤ med ≤ max: 36 ≤ 10897 ≤ 1.53e+08 IQR (CV) : 26528 (19.5)	3118 distinct values		3272 (99.8%)	7 (0.2%)
123	UnempRate2011 [numeric]	Mean (sd) : 9 (3.4) min ≤ med ≤ max: 1.4 ≤ 8.7 ≤ 28.9 IQR (CV) : 4 (0.4)	200 distinct values		3272 (99.8%)	7 (0.2%)
124	NumCivLaborForce2011 [integer]	Mean (sd) : 142130 (2762563) min ≤ med ≤ max: 66 ≤ 12016 ≤ 1.55e+08 IQR (CV) : 28183 (19.4)	3123 distinct values		3272 (99.8%)	7 (0.2%)
125	NumEmployed2011 [integer]	Mean (sd) : 129380 (2514380) min ≤ med ≤ max: 62 ≤ 10836 ≤ 1.41e+08 IQR (CV) : 25612 (19.4)	3120 distinct values		3272 (99.8%)	7 (0.2%)
126	NumCivLaborForce2012 [integer]	Mean (sd) : 142593 (2772051) min ≤ med ≤ max: 67 ≤ 11960 ≤ 1.55e+08 IQR (CV) : 27825 (19.4)	3141 distinct values		3272 (99.8%)	7 (0.2%)
127	NumUnemployed2010 [integer]	Mean (sd) : 13691 (266615) min ≤ med ≤ max: 4 ≤ 1258 ≤ 14862528 IQR (CV) : 2804 (19.5)	2325 distinct values		3272 (99.8%)	7 (0.2%)
128	NumCivLaborForce2008 [integer]	Mean (sd) : 141610 (2748841) min ≤ med ≤ max: 43 ≤ 12504 ≤ 1.54e+08 IQR (CV) : 28021 (19.4)	3140 distinct values		3267 (99.6%)	12 (0.4%)
129	NumUnemployed2011 [integer]	Mean (sd) : 12750 (248454) min ≤ med ≤ max: 4 ≤ 1174 ≤ 13840502 IQR (CV) : 2558 (19.5)	2276 distinct values		3272 (99.8%)	7 (0.2%)
130	NumEmployed2010 [integer]	Mean (sd) : 128146 (2489980) min ≤ med ≤ max: 67 ≤ 10868 ≤ 1.39e+08 IQR (CV) : 25460 (19.4)	3130 distinct values		3272 (99.8%)	7 (0.2%)
131	NumCivLaborForce2010 [integer]	Mean (sd) : 141838 (2756335) min ≤ med ≤ max: 71 ≤ 12098 ≤ 1.54e+08 IQR (CV) : 28236 (19.4)	3144 distinct values		3272 (99.8%)	7 (0.2%)
132	NumUnemployed2009 [integer]	Mean (sd) : 13129 (255206) min ≤ med ≤ max: 4 ≤ 1228 ≤ 14230942 IQR (CV) : 2736 (19.4)	2338 distinct values		3267 (99.6%)	12 (0.4%)
133	NumEmployed2009 [integer]	Mean (sd) : 128526 (2495118) min ≤ med ≤ max: 39 ≤ 11311 ≤ 1.4e+08 IQR (CV) : 25617 (19.4)	3128 distinct values		3267 (99.6%)	12 (0.4%)
134	NumCivLaborForce2009 [integer]	Mean (sd) : 141655 (2750109) min ≤ med ≤ max: 43 ≤ 12507 ≤ 1.54e+08 IQR (CV) : 28014 (19.4)	3151 distinct values		3267 (99.6%)	12 (0.4%)
135	UnempRate2008 [numeric]	Mean (sd) : 6 (2.4) min ≤ med ≤ max: 1.3 ≤ 5.7 ≤ 22.6 IQR (CV) : 2.7 (0.4)	148 distinct values		3267 (99.6%)	12 (0.4%)
136	UnempRate2012 [numeric]	Mean (sd) : 8.1 (3.2) min ≤ med ≤ max: 1.1 ≤ 7.8 ≤ 27.4 IQR (CV) : 3.7 (0.4)	189 distinct values		3272 (99.8%)	7 (0.2%)
137	NumEmployed2008 [integer]	Mean (sd) : 133388 (2589264) min ≤ med ≤ max: 40 ≤ 11701 ≤ 1.45e+08 IQR (CV) : 26457 (19.4)	3106 distinct values		3267 (99.6%)	12 (0.4%)
138	UnempRate2009 [numeric]	Mean (sd) : 9.3 (3.5) min ≤ med ≤ max: 2.1 ≤ 8.8 ≤ 27.4 IQR (CV) : 4.2 (0.4)	195 distinct values		3267 (99.6%)	12 (0.4%)
139	NumUnemployed2008 [integer]	Mean (sd) : 8222 (159719) min ≤ med ≤ max: 3 ≤ 788 ≤ 8900776 IQR (CV) : 1747 (19.4)	2043 distinct values		3267 (99.6%)	12 (0.4%)
140	NumUnemployed2015 [integer]	Mean (sd) : 7637 (148385) min ≤ med ≤ max: 4 ≤ 708 ≤ 8283796 IQR (CV) : 1582 (19.4)	1956 distinct values		3272 (99.8%)	7 (0.2%)
141	NumUnemployed2019 [integer]	Mean (sd) : 5515 (107123) min ≤ med ≤ max: 4 ≤ 499 ≤ 5984808 IQR (CV) : 1126 (19.4)	1740 distinct values		3272 (99.8%)	7 (0.2%)
142	NumCivLaborforce2019 [integer]	Mean (sd) : 149874 (2915158) min ≤ med ≤ max: 223 ≤ 11809 ≤ 1.63e+08 IQR (CV) : 28515 (19.5)	3140 distinct values		3272 (99.8%)	7 (0.2%)
143	NumUnemployed2018 [integer]	Mean (sd) : 5795 (112551) min ≤ med ≤ max: 4 ≤ 512 ≤ 6286707 IQR (CV) : 1166 (19.4)	1773 distinct values		3272 (99.8%)	7 (0.2%)
144	NumEmployed2018 [integer]	Mean (sd) : 142510 (2772143) min ≤ med ≤ max: 205 ≤ 11216 ≤ 1.55e+08 IQR (CV) : 27049 (19.5)	3133 distinct values		3272 (99.8%)	7 (0.2%)
145	NumCivLaborforce2018 [integer]	Mean (sd) : 148305 (2884660) min ≤ med ≤ max: 211 ≤ 11777 ≤ 1.61e+08 IQR (CV) : 28284 (19.5)	3137 distinct values		3272 (99.8%)	7 (0.2%)
146	NumUnemployed2017 [integer]	Mean (sd) : 6432 (124919) min ≤ med ≤ max: 5 ≤ 570 ≤ 6975103 IQR (CV) : 1334 (19.4)	1840 distinct values		3272 (99.8%)	7 (0.2%)
147	NumEmployed2017 [integer]	Mean (sd) : 140751 (2737799) min ≤ med ≤ max: 95 ≤ 11135 ≤ 1.53e+08 IQR (CV) : 26906 (19.5)	3124 distinct values		3272 (99.8%)	7 (0.2%)
148	NumCivLaborforce2017 [integer]	Mean (sd) : 147183 (2862681) min ≤ med ≤ max: 100 ≤ 11735 ≤ 1.6e+08 IQR (CV) : 28049 (19.4)	3146 distinct values		3272 (99.8%)	7 (0.2%)
149	NumUnemployed2016 [integer]	Mean (sd) : 7122 (138304) min ≤ med ≤ max: 4 ≤ 660 ≤ 7723517 IQR (CV) : 1502 (19.4)	1938 distinct values		3272 (99.8%)	7 (0.2%)
150	NumEmployed2016 [integer]	Mean (sd) : 138662 (2696926) min ≤ med ≤ max: 82 ≤ 11035 ≤ 1.51e+08 IQR (CV) : 26506 (19.4)	3116 distinct values		3272 (99.8%)	7 (0.2%)
151	NumCivLaborforce2016 [integer]	Mean (sd) : 145784 (2835184) min ≤ med ≤ max: 86 ≤ 11670 ≤ 1.59e+08 IQR (CV) : 28034 (19.4)	3112 distinct values		3272 (99.8%)	7 (0.2%)
152	NumCivLaborforce2013 [integer]	Mean (sd) : 142920 (2778954) min ≤ med ≤ max: 75 ≤ 11868 ≤ 1.55e+08 IQR (CV) : 27642 (19.4)	3131 distinct values		3272 (99.8%)	7 (0.2%)
153	NumEmployed2015 [integer]	Mean (sd) : 136473 (2654156) min ≤ med ≤ max: 73 ≤ 10904 ≤ 1.49e+08 IQR (CV) : 26088 (19.4)	3117 distinct values		3272 (99.8%)	7 (0.2%)
154	NumEmployed2012 [integer]	Mean (sd) : 131061 (2547581) min ≤ med ≤ max: 63 ≤ 10944 ≤ 1.43e+08 IQR (CV) : 25719 (19.4)	3129 distinct values		3272 (99.8%)	7 (0.2%)
155	NumUnemployed2014 [integer]	Mean (sd) : 8868 (172446) min ≤ med ≤ max: 4 ≤ 816 ≤ 9618987 IQR (CV) : 1809 (19.4)	2040 distinct values		3272 (99.8%)	7 (0.2%)
156	NumEmployed2014 [integer]	Mean (sd) : 134474 (2615176) min ≤ med ≤ max: 75 ≤ 10842 ≤ 1.46e+08 IQR (CV) : 26012 (19.4)	3113 distinct values		3272 (99.8%)	7 (0.2%)
157	NumCivLaborforce2014 [integer]	Mean (sd) : 143342 (2787500) min ≤ med ≤ max: 79 ≤ 11694 ≤ 1.56e+08 IQR (CV) : 27584 (19.4)	3142 distinct values		3272 (99.8%)	7 (0.2%)
158	UnempRate2013 [numeric]	Mean (sd) : 7.6 (3.1) min ≤ med ≤ max: 1.2 ≤ 7.3 ≤ 27.4 IQR (CV) : 3.6 (0.4)	196 distinct values		3272 (99.8%)	7 (0.2%)
159	NumUnemployed2013 [integer]	Mean (sd) : 10566 (205637) min ≤ med ≤ max: 4 ≤ 964 ≤ 11467539 IQR (CV) : 2118 (19.5)	2154 distinct values		3272 (99.8%)	7 (0.2%)
160	NumEmployed2019 [integer]	Mean (sd) : 144359 (2808078) min ≤ med ≤ max: 212 ≤ 11277 ≤ 1.57e+08 IQR (CV) : 27347 (19.5)	3107 distinct values		3272 (99.8%)	7 (0.2%)
161	NumEmployed2013 [integer]	Mean (sd) : 132354 (2573464) min ≤ med ≤ max: 71 ≤ 10807 ≤ 1.44e+08 IQR (CV) : 25757 (19.4)	3130 distinct values		3272 (99.8%)	7 (0.2%)
162	NumUnemployed2007 [integer]	Mean (sd) : 6508 (126039) min ≤ med ≤ max: 3 ≤ 650 ≤ 7035039 IQR (CV) : 1462 (19.4)	1909 distinct values		3267 (99.6%)	12 (0.4%)
163	NumEmployed2007 [integer]	Mean (sd) : 133673 (2594574) min ≤ med ≤ max: 38 ≤ 11744 ≤ 1.45e+08 IQR (CV) : 26580 (19.4)	3103 distinct values		3267 (99.6%)	12 (0.4%)
164	NumCivLaborforce2007 [integer]	Mean (sd) : 140181 (2720538) min ≤ med ≤ max: 41 ≤ 12420 ≤ 1.52e+08 IQR (CV) : 27822 (19.4)	3132 distinct values		3267 (99.6%)	12 (0.4%)
165	NumUnemployed2012 [integer]	Mean (sd) : 11532 (224694) min ≤ med ≤ max: 4 ≤ 1044 ≤ 12518797 IQR (CV) : 2281 (19.5)	2221 distinct values		3272 (99.8%)	7 (0.2%)
166	NumCivLaborforce2015 [integer]	Mean (sd) : 144110 (2802464) min ≤ med ≤ max: 77 ≤ 11598 ≤ 1.57e+08 IQR (CV) : 27728 (19.4)	3119 distinct values		3272 (99.8%)	7 (0.2%)
167	RuralUrbanContinuumCode2013 [integer]	Mean (sd) : 4.9 (2.7) min ≤ med ≤ max: 1 ≤ 6 ≤ 9 IQR (CV) : 5 (0.6)	1 : 472 ( 14.6% ) 2 : 396 ( 12.3% ) 3 : 369 ( 11.5% ) 4 : 217 ( 6.7% ) 5 : 92 ( 2.9% ) 6 : 597 ( 18.5% ) 7 : 434 ( 13.5% ) 8 : 220 ( 6.8% ) 9 : 425 ( 13.2% )		3222 (98.3%)	57 (1.7%)
168	UrbanInfluenceCode2013 [integer]	Mean (sd) : 5.2 (3.5) min ≤ med ≤ max: 1 ≤ 5 ≤ 12 IQR (CV) : 6 (0.7)	12 distinct values		3222 (98.3%)	57 (1.7%)
169	RuralUrbanContinuumCode2003 [integer]	Mean (sd) : 5.1 (2.7) min ≤ med ≤ max: 1 ≤ 6 ≤ 9 IQR (CV) : 4 (0.5)	1 : 455 ( 14.1% ) 2 : 336 ( 10.4% ) 3 : 368 ( 11.4% ) 4 : 221 ( 6.9% ) 5 : 105 ( 3.3% ) 6 : 613 ( 19.0% ) 7 : 453 ( 14.0% ) 8 : 235 ( 7.3% ) 9 : 439 ( 13.6% )		3225 (98.4%)	54 (1.6%)
170	UrbanInfluenceCode2003 [integer]	Mean (sd) : 5.4 (3.5) min ≤ med ≤ max: 1 ≤ 5 ≤ 12 IQR (CV) : 6 (0.6)	12 distinct values		3225 (98.4%)	54 (1.6%)
171	Metro2013 [integer]	Min : 0 Mean : 0.4 Max : 1	0 : 1985 ( 61.6% ) 1 : 1237 ( 38.4% )		3222 (98.3%)	57 (1.7%)
172	Nonmetro2013 [integer]	Min : 0 Mean : 0.6 Max : 1	0 : 1237 ( 38.4% ) 1 : 1985 ( 61.6% )		3222 (98.3%)	57 (1.7%)
173	Micropolitan2013 [integer]	Min : 0 Mean : 0.2 Max : 1	0 : 2576 ( 80.0% ) 1 : 646 ( 20.0% )		3222 (98.3%)	57 (1.7%)
174	Type_2015_Update [integer]	Mean (sd) : 1.8 (1.8) min ≤ med ≤ max: 0 ≤ 1 ≤ 5 IQR (CV) : 3 (1)	0 : 1237 ( 39.4% ) 1 : 444 ( 14.1% ) 2 : 221 ( 7.0% ) 3 : 501 ( 15.9% ) 4 : 407 ( 12.9% ) 5 : 333 ( 10.6% )		3143 (95.9%)	136 (4.1%)
175	Type_2015_Farming_NO [integer]	Min : 0 Mean : 0.1 Max : 1	0 : 2699 ( 85.9% ) 1 : 444 ( 14.1% )		3143 (95.9%)	136 (4.1%)
176	Type_2015_Manufacturing_NO [integer]	Min : 0 Mean : 0.2 Max : 1	0 : 2642 ( 84.1% ) 1 : 501 ( 15.9% )		3143 (95.9%)	136 (4.1%)
177	Type_2015_Mining_NO [integer]	Min : 0 Mean : 0.1 Max : 1	0 : 2922 ( 93.0% ) 1 : 221 ( 7.0% )		3143 (95.9%)	136 (4.1%)
178	Type_2015_Government_NO [integer]	Min : 0 Mean : 0.1 Max : 1	0 : 2736 ( 87.1% ) 1 : 407 ( 12.9% )		3143 (95.9%)	136 (4.1%)
179	Type_2015_Recreation_NO [integer]	Min : 0 Mean : 0.1 Max : 1	0 : 2810 ( 89.4% ) 1 : 333 ( 10.6% )		3143 (95.9%)	136 (4.1%)
180	Low_Education_2015_update [integer]	Min : 0 Mean : 0.1 Max : 1	0 : 2676 ( 85.1% ) 1 : 467 ( 14.9% )		3143 (95.9%)	136 (4.1%)
181	Low_Employment_2015_update [integer]	Min : 0 Mean : 0.3 Max : 1	0 : 2237 ( 71.2% ) 1 : 906 ( 28.8% )		3143 (95.9%)	136 (4.1%)
182	Population_loss_2015_update [integer]	Min : 0 Mean : 0.2 Max : 1	0 : 2614 ( 83.2% ) 1 : 529 ( 16.8% )		3143 (95.9%)	136 (4.1%)
183	Retirement_Destination_2015_Update [integer]	Min : 0 Mean : 0.1 Max : 1	0 : 2701 ( 85.9% ) 1 : 442 ( 14.1% )		3143 (95.9%)	136 (4.1%)
184	Perpov_1980_0711 [integer]	Min : 0 Mean : 0.1 Max : 1	0 : 2790 ( 88.8% ) 1 : 353 ( 11.2% )		3143 (95.9%)	136 (4.1%)
185	PersistentChildPoverty_1980_2011 [integer]	Min : 0 Mean : 0.2 Max : 1	0 : 2435 ( 77.5% ) 1 : 708 ( 22.5% )		3143 (95.9%)	136 (4.1%)
186	Hipov [integer]	Mean (sd) : 0.2 (0.5) min ≤ med ≤ max: -9 ≤ 0 ≤ 1 IQR (CV) : 0 (2)	-9 : 1 ( 0.0% ) 0 : 2482 ( 77.1% ) 1 : 738 ( 22.9% )		3221 (98.2%)	58 (1.8%)
187	HiAmenity [integer]	Min : 0 Mean : 0.3 Max : 1	0 : 2330 ( 75.0% ) 1 : 777 ( 25.0% )		3107 (94.8%)	172 (5.2%)
188	HiCreativeClass2000 [integer]	Min : 0 Mean : 0.3 Max : 1	0 : 2353 ( 75.0% ) 1 : 786 ( 25.0% )		3139 (95.7%)	140 (4.3%)
189	Gas_Change [integer]	Mean (sd) : 0.6 (2) min ≤ med ≤ max: 0 ≤ 0 ≤ 9 IQR (CV) : 0 (3.5)	0 : 2780 ( 89.4% ) 2 : 174 ( 5.6% ) 9 : 155 ( 5.0% )		3109 (94.8%)	170 (5.2%)
190	Oil_Change [integer]	Mean (sd) : 0.4 (1.8) min ≤ med ≤ max: 0 ≤ 0 ≤ 9 IQR (CV) : 0 (4.2)	0 : 2880 ( 92.6% ) 2 : 107 ( 3.4% ) 9 : 122 ( 3.9% )		3109 (94.8%)	170 (5.2%)
191	Oil_Gas_Change [integer]	Mean (sd) : 0.8 (2.3) min ≤ med ≤ max: 0 ≤ 0 ≤ 9 IQR (CV) : 0 (3)	0 : 2679 ( 86.2% ) 2 : 218 ( 7.0% ) 9 : 212 ( 6.8% )		3109 (94.8%)	170 (5.2%)
192	Metro2003 [integer]	Min : 0 Mean : 0.4 Max : 1	0 : 2066 ( 64.1% ) 1 : 1159 ( 35.9% )		3225 (98.4%)	54 (1.6%)
193	NonmetroNotAdj2003 [integer]	Min : 0 Mean : 0.3 Max : 1	0 : 2228 ( 69.1% ) 1 : 997 ( 30.9% )		3225 (98.4%)	54 (1.6%)
194	NonmetroAdj2003 [integer]	Min : 0 Mean : 0.3 Max : 1	0 : 2155 ( 66.8% ) 1 : 1070 ( 33.2% )		3225 (98.4%)	54 (1.6%)
195	Noncore2003 [integer]	Min : 0 Mean : 0.4 Max : 1	0 : 1839 ( 57.0% ) 1 : 1386 ( 43.0% )		3225 (98.4%)	54 (1.6%)
196	EconomicDependence2000 [integer]	Mean (sd) : 3.9 (1.7) min ≤ med ≤ max: 1 ≤ 4 ≤ 6 IQR (CV) : 3 (0.4)	1 : 440 ( 14.0% ) 2 : 128 ( 4.1% ) 3 : 904 ( 28.8% ) 4 : 381 ( 12.1% ) 5 : 340 ( 10.8% ) 6 : 948 ( 30.2% )		3141 (95.8%)	138 (4.2%)
197	Nonmetro2003 [integer]	Min : 0 Mean : 0.6 Max : 1	0 : 1159 ( 35.9% ) 1 : 2066 ( 64.1% )		3225 (98.4%)	54 (1.6%)
198	Micropolitan2003 [integer]	Min : 0 Mean : 0.2 Max : 1	0 : 2545 ( 78.9% ) 1 : 680 ( 21.1% )		3225 (98.4%)	54 (1.6%)
199	FarmDependent2003 [integer]	Min : 0 Mean : 0.1 Max : 1	0 : 2701 ( 86.0% ) 1 : 440 ( 14.0% )		3141 (95.8%)	138 (4.2%)
200	ManufacturingDependent2000 [integer]	Min : 0 Mean : 0.3 Max : 1	0 : 2237 ( 71.2% ) 1 : 904 ( 28.8% )		3141 (95.8%)	138 (4.2%)
201	LowEducation2000 [integer]	Min : 0 Mean : 0.2 Max : 1	0 : 2519 ( 80.2% ) 1 : 622 ( 19.8% )		3141 (95.8%)	138 (4.2%)
202	RetirementDestination2000 [integer]	Min : 0 Mean : 0.1 Max : 1	0 : 2701 ( 86.0% ) 1 : 440 ( 14.0% )		3141 (95.8%)	138 (4.2%)
203	PersistentPoverty2000 [integer]	Min : 0 Mean : 0.1 Max : 1	0 : 2755 ( 87.7% ) 1 : 386 ( 12.3% )		3141 (95.8%)	138 (4.2%)
204	Noncore2013 [integer]	Min : 0 Mean : 0.4 Max : 1	0 : 1883 ( 58.4% ) 1 : 1339 ( 41.6% )		3222 (98.3%)	57 (1.7%)
205	Type_2015_Nonspecialized_NO [integer]	Min : 0 Mean : 0.4 Max : 1	0 : 1906 ( 60.6% ) 1 : 1237 ( 39.4% )		3143 (95.9%)	136 (4.1%)
206	Metro_Adjacent2013 [integer]	Min : 0 Mean : 0.3 Max : 1	0 : 2194 ( 68.1% ) 1 : 1028 ( 31.9% )		3222 (98.3%)	57 (1.7%)
207	PersistentChildPoverty2004 [integer]	Min : 0 Mean : 0.2 Max : 1	0 : 2407 ( 76.6% ) 1 : 734 ( 23.4% )		3141 (95.8%)	138 (4.2%)
208	RecreationDependent2000 [integer]	Min : 0 Mean : 0.1 Max : 1	0 : 2807 ( 89.4% ) 1 : 334 ( 10.6% )		3141 (95.8%)	138 (4.2%)

Generated by summarytools 1.0.0 (R version 4.1.2)
2022-02-27

Covid_rate data set has 10008984 observations and 8 variables; it is a wide panel data with a time interval from 2020-01-21 to 2021-02-20. County_data data set has 3279 observations and 208 variables. It is a cross-sectional data with 3279 counties. The missing values are not prevalent in these two data sets.

2.2 covid case trend

2.2.1 three states, by day and state

# unique(covid_rate$State)
covid.3state.day = covid_rate[State %in% c("New York","Washington","Florida"),.(
  cum_cases = sum(cum_cases),
  cum_deaths = sum(cum_deaths),
  week = mean(week)
),by = .(date,State)]
covid.3state.day = covid.3state.day[order(list(State,date))]

covid.3state.day[,new_cases := c(NA,diff(cum_cases)),by = State]
covid.3state.day[,date := ymd(date)]
ggplot(covid.3state.day,aes(x=date,y=new_cases,group=State,color=State))+
  geom_line()+
  scale_x_date(date_breaks = "3 month",date_labels = "%Y-%m")+
  labs(title = "New Cases Trends for NY, WA and FL")+
  theme_bw()

The biggest problem: daily variability is extremely high, making the trends zigzagging. Maybe there is an innate difference among days in a week because people have different work and life style in different days. We may wish to smooth out these excessive noise by aggregating in the weekly level.

2.2.2 Spaghetti Plots

# check
covid_rate[State == "New York",length(County),by = .(State,date)] # problem: some counties do not report cases in some days. New added counties cause problems

##         State       date V1
##   1: New York 2020-03-12 17
##   2: New York 2020-03-13 18
##   3: New York 2020-03-14 21
##   4: New York 2020-03-15 25
##   5: New York 2020-03-16 28
##  ---                       
## 354: New York 2020-03-07  9
## 355: New York 2020-03-08 11
## 356: New York 2020-03-09 11
## 357: New York 2020-03-10 11
## 358: New York 2020-03-11 12

We find that the number of counties reporting cases every day is increasing. We may want to adjust the total population accordingly.

covid.weekend = covid_rate[,.(
  cum_cases_weekend = cum_cases[length(cum_cases)],
  cum_deaths_weekend = cum_deaths[length(cum_deaths)],
  TotalPopEst2019.weekend = TotalPopEst2019[length(TotalPopEst2019)]
), by = .(week,State,County)]
covid.weekend = covid.weekend[order(list(State,County,week))]
covid.weekend[,":="(new_cases = c(NA,diff(cum_cases_weekend)),
                                 new_deaths = c(NA,diff(cum_deaths_weekend))),
                           by = .(State,County)]
covid.week = covid.weekend[!is.na(new_cases)&!is.na(new_deaths),.(
  new_cases = sum(new_cases),
  new_deaths = sum(new_deaths),
  TotalPopEst2019 = sum(TotalPopEst2019.weekend)
),by = .(State,week)]
covid.week[,weekly_case_per100k := new_cases/TotalPopEst2019*100000]

# data.ma = covid_rate[State == "Massachusetts"] # pay attention: week 33 of MA

ggplot(covid.week,aes(x=week,y=weekly_case_per100k,group=State,color=State))+
  geom_line()+
  labs(title = "Spaghetti Plots, Weekly New Cases")+
  theme_bw()

2.2.3 Summary

There are two possibilities to explain this. Firstly, many states, such as those in the Northeastern part of California, have densely populated urban centers. COVID tends to spread a lot quicker in these areas. Secondly, some states imposed stricter lockdown measures and mask-mandates early on to combat the COVID pandemic. These initiatives likely slowed the spread of COVID.

2.2.4 Effectiveness of lockdown by graphs

# summary(covid_intervention)
# some examples

covid_intervention[STATE == "New York"]

## Empty data.table (0 rows and 16 cols): FIPS,STATE,AREA_NAME,stay at home,>50 gatherings,>500 gatherings...

covid_intervention_state = covid_intervention[substr(FIPS,nchar(FIPS)-2,nchar(FIPS)) == "000"]

# NY
ggplot(covid.3state.day[State == "New York"],aes(x=date,y=new_cases))+
  geom_line()+
  scale_x_date(date_breaks = "3 month",date_labels = "%Y-%m")+
  geom_vline(xintercept = covid_intervention_state[STATE == "NY","stay at home"][[1,1]],color = "red",lty = 5)+
  labs(title = "New Cases Trends for NY")+
  theme_bw()

# FL
ggplot(covid.3state.day[State == "Florida"],aes(x=date,y=new_cases))+
  geom_line()+
  scale_x_date(date_breaks = "3 month",date_labels = "%Y-%m")+
  geom_vline(xintercept = covid_intervention_state[STATE == "FL","stay at home"][[1,1]],color = "red",lty = 5)+
  labs(title = "New Cases Trends for FL")+
  theme_bw()

The graphs for these two states indicate that the lockdown policy may have some positive effects on slowing down the spread of the virus.

2.3 covid death trend

2.3.1 Monthly deaths per 100k heatmap

# pay attention to numbers smaller than zero
covid_rate = covid_rate[order(FIPS,date)]
covid_rate[,":="(new_cases = c(NA,diff(cum_cases)),
                 new_deaths = c(NA,diff(cum_deaths)),
                 year = year(date),
                 month = month(date),
                year.month = round_date(date,"month")),by = FIPS]
covid.month = covid_rate[!is.na(new_cases)&!is.na(new_deaths),.(
  new_cases = sum(new_cases),
  new_deaths = sum(new_deaths),
  TotalPopEst2019 = TotalPopEst2019[length(TotalPopEst2019)]
),by = .(State,County,year,month)]
covid.month = covid.month[,.(
  new_cases = sum(new_cases),
  new_deaths = sum(new_deaths),
  TotalPopEst2019 = sum(TotalPopEst2019)
),by = .(State,year,month)]

covid.month[,monthly_death_per100k := new_deaths/TotalPopEst2019*100000]

Here we only give one example: 2020-9. The plots for all months are shown in (ii).

covid.death.plot.list = list()
setnames(covid.month,"State","state")
max_col = quantile(covid.month$monthly_death_per100k,1,na.rm = T)
min_col = quantile(covid.month$monthly_death_per100k,0,na.rm = T)
for (i in 2:12) {
  covid.death.plot.list[[i-1]] =
    plot_usmap(regions = "state",data = covid.month[year == 2020 & month == i],
               values = "monthly_death_per100k", exclude = c("Hawaii", "Alaska"),color = "black") + 
    scale_fill_distiller(
      palette = "Reds",direction = 1,
      name = "Number of New Covid Deaths per 100,000 People", 
      limits = c(min_col, max_col)) + 
    labs(title = paste0("New Covid Deaths, 2020-",i), subtitle = "Continental US States") +
    theme(legend.position = "right")
}

ggplotly(covid.death.plot.list[[8]])

# plot_usmap(regions = "state",data = covid.month[year == 2020 & month == i],
#                values = "monthly_death_per100k", exclude = c("Hawaii", "Alaska"),color = "black") + 
#     scale_fill_gradient(
#       low = "white", high = "red", 
#       name = "Number of New Covid Deaths per 100,000 People", 
#       label = scales::comma) + 
#     labs(title = paste0("New Covid Deaths, 2020-",i), subtitle = "Continental US States") +
#     theme(legend.position = "right")

2.3.2 Animations

# plotly
abbr = unique(us_map(regions =
"states") %>% select(abbr, full)) 

plotly.data = covid.month[year == 2020,.(month,state,monthly_death_per100k)] %>%
  mutate(hover =  paste(state, '<br>', 
                        'new covid deaths', round(monthly_death_per100k, 3))) %>% 
  left_join(abbr,by = c("state" = "full"))

# give state boundaries a white border
l <- list(color = toRGB("white"), width = 2)
# specify some map projection/options
g <- list(
  scope = 'usa',
  projection = list(type = 'albers usa'),
  showlakes = TRUE,
  lakecolor = toRGB('white'),
  exclude = c("")
)

fig <- plot_geo(plotly.data, locationmode = 'USA-states')
fig <- fig %>% add_trace(
    z = ~monthly_death_per100k, text = ~hover, locations = ~abbr,
    color = ~monthly_death_per100k, colors = 'Reds',
    zmin = min_col, zmax = max_col,frame = ~month
  )

fig <- fig %>% colorbar(title = "Monthly new covid deaths of state")
fig <- fig %>% layout(
    title = 'Monthly new covid deaths of state',
    geo = g,
    hoverlabel = list(bgcolor="white")
  )
fig

save.image("codes/hw3_covid.RData")

load("codes/hw3_covid.RData")

2.4 covid factor

county.covid = covid_rate[date == as.Date("2021-02-01"),.(
  FIPS,County,State,
  total_death_per100k = cum_deaths/TotalPopEst2019*100000
)] %>% 
  right_join(county_data, by = "FIPS") %>%
  mutate(log_total_death_per100k = log(total_death_per100k + 1))

county.covid.sub <- county.covid %>%
  select(log_total_death_per100k,State.x,County.x, FIPS, Deep_Pov_All, PovertyAllAgesPct, PerCapitaInc, UnempRate2019, PctEmpFIRE, PctEmpConstruction, PctEmpTrans, PctEmpMining, PctEmpTrade, PctEmpInformation, PctEmpAgriculture, PctEmpManufacturing, PctEmpServices, PopDensity2010, OwnHomePct, Age65AndOlderPct2010, TotalPop25Plus, Under18Pct2010, Ed2HSDiplomaOnlyPct, Ed3SomeCollegePct, Ed4AssocDegreePct, Ed5CollegePlusPct, ForeignBornPct, Net_International_Migration_Rate_2010_2019, NetMigrationRate1019, NaturalChangeRate1019, TotalPopEst2019, WhiteNonHispanicPct2010, NativeAmericanNonHispanicPct2010, BlackNonHispanicPct2010, AsianNonHispanicPct2010, HispanicPct2010, Type_2015_Update, RuralUrbanContinuumCode2013, UrbanInfluenceCode2013, Perpov_1980_0711, HiCreativeClass2000, HiAmenity, Retirement_Destination_2015_Update)

setnames(county.covid.sub,c("State.x","County.x"),c("state","county"))

Num of missings in every variable

# county.covid.sub[is.na(state)]
apply(is.na(county.covid.sub), 2, sum) # missing in state, county: all aggregate states, puerto rico, hawaii, alaska; bedford in Virginia has two obs, duplicated

##                    log_total_death_per100k 
##                                        171 
##                                      state 
##                                        171 
##                                     county 
##                                        171 
##                                       FIPS 
##                                          0 
##                               Deep_Pov_All 
##                                          6 
##                          PovertyAllAgesPct 
##                                         86 
##                               PerCapitaInc 
##                                          6 
##                              UnempRate2019 
##                                          7 
##                                 PctEmpFIRE 
##                                          7 
##                         PctEmpConstruction 
##                                          7 
##                                PctEmpTrans 
##                                          7 
##                               PctEmpMining 
##                                          7 
##                                PctEmpTrade 
##                                          7 
##                          PctEmpInformation 
##                                          7 
##                          PctEmpAgriculture 
##                                          7 
##                        PctEmpManufacturing 
##                                          7 
##                             PctEmpServices 
##                                          7 
##                             PopDensity2010 
##                                          6 
##                                 OwnHomePct 
##                                          6 
##                       Age65AndOlderPct2010 
##                                          6 
##                             TotalPop25Plus 
##                                          6 
##                             Under18Pct2010 
##                                          6 
##                        Ed2HSDiplomaOnlyPct 
##                                          6 
##                          Ed3SomeCollegePct 
##                                          6 
##                          Ed4AssocDegreePct 
##                                          6 
##                          Ed5CollegePlusPct 
##                                          6 
##                             ForeignBornPct 
##                                         85 
## Net_International_Migration_Rate_2010_2019 
##                                         85 
##                       NetMigrationRate1019 
##                                         85 
##                      NaturalChangeRate1019 
##                                         85 
##                            TotalPopEst2019 
##                                          6 
##                    WhiteNonHispanicPct2010 
##                                          6 
##           NativeAmericanNonHispanicPct2010 
##                                          6 
##                    BlackNonHispanicPct2010 
##                                          6 
##                    AsianNonHispanicPct2010 
##                                          6 
##                            HispanicPct2010 
##                                          6 
##                           Type_2015_Update 
##                                        136 
##                RuralUrbanContinuumCode2013 
##                                         57 
##                     UrbanInfluenceCode2013 
##                                         57 
##                           Perpov_1980_0711 
##                                        136 
##                        HiCreativeClass2000 
##                                        140 
##                                  HiAmenity 
##                                        172 
##         Retirement_Destination_2015_Update 
##                                        136

county.covid.sub = na.omit(county.covid.sub) # -174

2.4.1 lasso

set.seed(1)
model.var = model.matrix(log_total_death_per100k~.,data = county.covid.sub[,-c("FIPS","county")])[,-1] # no Alabama here
# head(model.test)
death = county.covid.sub[,log_total_death_per100k]
fit1.cv = cv.glmnet(model.var,death,alpha = 1, nfolds = 10, intercept = T,
                    penalty.factor = c(rep(0,48),rep(1,ncol(model.var)-48))) # alpha: the para in elastic net
coef.min = coef(fit1.cv,s="lambda.1se") # more parsimonious usually. If use min, maybe there is noise
# coef(fit1.cv,s="lambda.1min")
nonzero.coef = coef.min[which(coef.min!=0),]
# plot(fit1.cv)
nonzero.var = names(nonzero.coef)[-1]

2.4.2 Fine tune the model

Relaxed lasso result

data.selected = data.table(death,model.var[,which(colnames(model.var) %in% nonzero.var)])

fit.1se.lm = lm(death~.,data = data.selected)
# relaxed lasso
stargazer(fit.1se.lm,type=output_format, align=TRUE)

	Dependent variable:
	death
stateArizona	0.267
	(0.238)
stateArkansas	0.056
	(0.135)
stateCalifornia	-0.771***
	(0.159)
stateColorado	-0.357**
	(0.153)
stateConnecticut	0.178
	(0.303)
stateDelaware	-0.024
	(0.469)
stateDistrict of Columbia	0.520
	(0.807)
stateFlorida	0.031
	(0.147)
stateGeorgia	0.066
	(0.117)
stateIdaho	-0.322*
	(0.166)
stateIllinois	0.211
	(0.132)
stateIndiana	-0.074
	(0.134)
stateIowa	0.287**
	(0.134)
stateKansas	-0.628***
	(0.137)
stateKentucky	-0.756***
	(0.128)
stateLouisiana	0.375***
	(0.143)
stateMaine	-1.370***
	(0.225)
stateMaryland	-0.059
	(0.196)
stateMassachusetts	0.077
	(0.240)
stateMichigan	-0.147
	(0.135)
stateMinnesota	-0.157
	(0.138)
stateMississippi	0.264**
	(0.132)
stateMissouri	-0.378***
	(0.129)
stateMontana	0.547***
	(0.158)
stateNebraska	-0.386***
	(0.143)
stateNevada	-0.577**
	(0.227)
stateNew Hampshire	-0.806***
	(0.273)
stateNew Jersey	0.329
	(0.209)
stateNew Mexico	-0.653***
	(0.192)
stateNew York	-0.367**
	(0.151)
stateNorth Carolina	-0.368***
	(0.127)
stateNorth Dakota	0.950***
	(0.166)
stateOhio	-0.523***
	(0.134)
stateOklahoma	-0.374***
	(0.137)
stateOregon	-0.865***
	(0.174)
statePennsylvania	0.039
	(0.146)
stateRhode Island	-0.177
	(0.372)
stateSouth Carolina	-0.011
	(0.153)
stateSouth Dakota	0.809***
	(0.151)
stateTennessee	0.058
	(0.130)
stateTexas	0.168
	(0.127)
stateUtah	-1.090***
	(0.196)
stateVermont	-2.140***
	(0.239)
stateVirginia	-0.476***
	(0.123)
stateWashington	-0.857***
	(0.168)
stateWest Virginia	-0.678***
	(0.155)
stateWisconsin	-0.134
	(0.140)
stateWyoming	0.208
	(0.205)
PovertyAllAgesPct	0.003
	(0.005)
PerCapitaInc	-0.00001
	(0.00001)
PctEmpConstruction	-0.049***
	(0.007)
PctEmpMining	-0.019***
	(0.006)
PctEmpAgriculture	-0.039***
	(0.004)
PctEmpManufacturing	0.003
	(0.003)
PopDensity2010	0.00003***
	(0.00001)
Age65AndOlderPct2010	0.034***
	(0.008)
Under18Pct2010	0.060***
	(0.008)
Ed3SomeCollegePct	-0.021***
	(0.005)
Ed5CollegePlusPct	-0.011***
	(0.004)
NetMigrationRate1019	-0.012***
	(0.003)
NaturalChangeRate1019	-0.044***
	(0.010)
WhiteNonHispanicPct2010	-0.003*
	(0.002)
HispanicPct2010	0.009***
	(0.002)
Type_2015_Update	-0.019**
	(0.009)
Constant	4.530***
	(0.417)
Observations	3,105
R2	0.359
Adjusted R2	0.345
Residual Std. Error	0.790 (df = 3040)
F Statistic	26.600*** (df = 64; 3040)
Note:	p<0.1; p<0.05; p<0.01

BIC graphs

fit.final.1 =  regsubsets(death~.,data = data.selected,method = "exhaustive",
                          nvmax = ncol(data.selected)-1,force.in = c(1:48),really.big = T) # compared to Arizona

summary.fit.final.1 = summary(fit.final.1)
plot(summary.fit.final.1$bic)

opt.index = 10 # with bic

We choose \(p=10\) by BIC criteria.

Final model after fine tuning

bic.var.select = summary.fit.final.1$which[opt.index,-1]
bic.var = names(bic.var.select)[which(bic.var.select)] 
# bic.var
final.expr = as.formula(paste("death", "~", paste(bic.var, collapse = "+"))) 
fit.final.2 = lm(final.expr,data = data.selected)

stargazer(fit.final.2,type=output_format, align=TRUE)

	Dependent variable:
	death
stateArizona	0.208
	(0.237)
stateArkansas	0.021
	(0.134)
stateCalifornia	-0.863***
	(0.155)
stateColorado	-0.434***
	(0.150)
stateConnecticut	0.070
	(0.299)
stateDelaware	-0.099
	(0.469)
stateDistrict of Columbia	0.657
	(0.804)
stateFlorida	-0.016
	(0.142)
stateGeorgia	0.053
	(0.116)
stateIdaho	-0.399**
	(0.163)
stateIllinois	0.107
	(0.127)
stateIndiana	-0.183
	(0.128)
stateIowa	0.178
	(0.129)
stateKansas	-0.706***
	(0.133)
stateKentucky	-0.841***
	(0.121)
stateLouisiana	0.371***
	(0.141)
stateMaine	-1.490***
	(0.222)
stateMaryland	-0.157
	(0.191)
stateMassachusetts	-0.005
	(0.238)
stateMichigan	-0.237*
	(0.132)
stateMinnesota	-0.268**
	(0.133)
stateMississippi	0.309**
	(0.131)
stateMissouri	-0.459***
	(0.123)
stateMontana	0.485***
	(0.155)
stateNebraska	-0.482***
	(0.138)
stateNevada	-0.647***
	(0.226)
stateNew Hampshire	-0.950***
	(0.271)
stateNew Jersey	0.254
	(0.203)
stateNew Mexico	-0.725***
	(0.190)
stateNew York	-0.429***
	(0.142)
stateNorth Carolina	-0.387***
	(0.126)
stateNorth Dakota	0.848***
	(0.161)
stateOhio	-0.632***
	(0.129)
stateOklahoma	-0.400***
	(0.136)
stateOregon	-0.932***
	(0.172)
statePennsylvania	-0.068
	(0.140)
stateRhode Island	-0.287
	(0.370)
stateSouth Carolina	-0.001
	(0.152)
stateSouth Dakota	0.738***
	(0.148)
stateTennessee	-0.003
	(0.128)
stateTexas	0.119
	(0.126)
stateUtah	-1.200***
	(0.188)
stateVermont	-2.280***
	(0.236)
stateVirginia	-0.516***
	(0.121)
stateWashington	-0.923***
	(0.167)
stateWest Virginia	-0.792***
	(0.148)
stateWisconsin	-0.252*
	(0.136)
stateWyoming	0.106
	(0.203)
PctEmpConstruction	-0.057***
	(0.007)
PctEmpMining	-0.024***
	(0.005)
PctEmpAgriculture	-0.041***
	(0.003)
Age65AndOlderPct2010	0.032***
	(0.008)
Under18Pct2010	0.060***
	(0.007)
Ed3SomeCollegePct	-0.024***
	(0.005)
Ed5CollegePlusPct	-0.016***
	(0.002)
NetMigrationRate1019	-0.014***
	(0.002)
NaturalChangeRate1019	-0.040***
	(0.010)
HispanicPct2010	0.011***
	(0.002)
Constant	4.520***
	(0.267)
Observations	3,105
R2	0.354
Adjusted R2	0.342
Residual Std. Error	0.792 (df = 3046)
F Statistic	28.800*** (df = 58; 3046)
Note:	p<0.1; p<0.05; p<0.01

# all significant

Age65AnOlderPct2010 has a significantly positive coefficient. However, Under18Pct2010 also has a significantly positive coefficient and is larger than that for elderly. This does not give strong support to the argument that covid affects the elderly the most; we would rather interpret it as, covid affect the middle ages the least.

BlackPct is not in the regression after controlling for existing variables while HispanicPct is in the regression. The coefficient for it is significantly positive, indicating that a higher Hispanic percentage in the region is connected with a higher fatal rate of covid. The analysis gives some support on a higher fatal rate in Hispanic group; it is not very clear for the black group.

2.4.3 diagnosis

scatter.list = list()

for (i in 49:58) { # cannot do this. the plot is built only after it's invoked if in the loop? Use aes_string
  name = bic.var[i]
  scatter.list[[i-48]] = ggplot(data.selected,aes_string(x=name,y="death"))+
    geom_point()+
    geom_smooth(method = "lm")+
    xlab(name)+
    ylab("log.new.death")+
    theme_bw()
}

Scatter Plots

plot_grid(plotlist = scatter.list)

# hist(county.covid$total_death_per100k,breaks = seq(0,900,10))

Residual Plot

# residual plot
plot(fit.final.2,1)

QQ Plot

# qq plot
plot(fit.final.2,2)

Seems not a good fit. Homoscedasticity is not well satisfied from the residual plot; from the residual plot we can see that the residuals have much thicker tails than the normal distribution.

2.4.4 Summary

We observe that controlling for other factors, a couple of the state predictors are statistically significant. In particular, we observe that states such as California, Colorado, Idaho, Kansas, Maine, Missouri, Nebraska, etc., have significant negative correlations. On the other hand, states like Mississippi and Louisiana all have significant positive correlations. The States with a higher COVID death rate tend to be Southern states with looser COVID restrictions and mask mandates. Despite having significantly higher population density, many States in the Northeast, such as Massachusetts and Vermont, fared better. This potentially suggests a strong case for COVID intervention. The government should continue to impose mask mandates and lockdown measures if a significant spike in cases happens in the future.

2.4.5 Improvements

From the scatter plots presented above, we can see that there are a lot of counties with zero in log total covid death per 100k and they are distant to other observations. Therefore, we may consider mixture models (for example, zero-inflated model) and classify them into two groups first, then make inference within every group.

As with the possible important variables, medical conditions could be one of them. Also total number of death per 100k may not be a perfect measure for our goal because it contains a part of randomness, i.e., the spread of covid in an area can have some random determinants; the virus might unexpectedly break out in some areas and result in a higher infection rate and mortality rate. We may want to complement the analysis with another dependent variable like \(\frac{TotalDeaths}{TotalCases}\).

2.4.6 Possible Imputations

Missing values are clustered in Puerto Rico, Alaska. These states are different in property with continent states so we may not trust the imputation results.